Evidence of Majorana fermions in the noise characteristic of normal metal–topological superconductor junctions

Abstract

A finite topological superconductor nanowire bears a Majorana fermion at its ends, leading to unique transport properties when connected to normal metal leads. We consider in this review two theoretical proposals based on noise measurements in normal metal–topological superconductor junctions. The first one considers a Hanbury Brown and Twiss setup where a topological superconductor is connected to two normal metal leads. The second proposal deals with the finite frequency noise of a single normal metal–topological superconductor junction. Both are computed using a unified framework of non equilibrium Keldysh Green’s functions using a Hamiltonian approach. Calculations are performed non-perturbatively in the tunnel hopping parameter and address both subgap and above gap regimes. Concerning the Hanbury Brown and Twiss setup, we find in the subgap case that when the two normal metal leads are biased with equal voltage, the noise crossed correlations are negative, as in the case of a three terminal normal metal junction. On the other hand when subgap voltages are opposite, the noise crossed correlations are positive. Predictions when the two Majoranas at the end of the topological superconductors hybridize, and when the chemical potential of the topological superconductor drives the system out of the topological phase are discussed. In the second proposal, the finite frequency emission and absorption noises are computed for a single junction. We observe noticeable structures in these quantities, related to simple transport processes involving the Majorana bound state. Both results offer an original tool for the further characterization of the presence of Majorana bound states in condensed matter systems.